Question

Solve the given equation. 5^(1/4)/125^(x/3) =1

Answer 1

Answer:

x = 0.25

Step-by-step explanation:

Rewrite the equation as:

$\frac{\sqrt[4]{5}}{125^{x/3}} = 1$

$\sqrt[4]{5} = 125^{x/3}$

$(\sqrt[4]{5})^4 = (125^{x/3})^4$

$5 = 125^{4x/3}$

$ln5 = ln(125^{4x/3})$

$ln5 = \frac{4x}{3}ln125$

$x = \frac{3}{4}\frac{ln5}{ln125} = \frac{3}{4}\frac{1}{3} = \frac{1}{4} = 0.25$